Asynchronous methods refer to parallel iterative procedures where each process performs its task without waiting for other processes to be completed, i.e., with whatever information it has locally available and with no synchronizations with other processes. In this talk, an asynchronous version of the optimized Schwarz method is presented for the solution of differential equations on a parallel computational environment. Convergence is proved under very mild conditions on the size of the subdomains, when approximate (non-optimal) interface conditions are utilized for Poisson’s equation on the plane. A different result for bounded rectangular domains is also shown. Numerical results are presented on large three-dimensional problems illustrating the efficiency of the proposed asynchronous parallel implementation of the method. The main application shown is the calculation of the gravitational potential in the area around the Chicxulub crater, in Yucatan, where an asteroid is believed to have landed 66 million years ago contributing to the extinction of the dinosaurs. (Joint work with Jos\’e Garay, Temple University; Fr\’ederic Magoul\’es and Cedric Venet, CentraleSupelec, Ch\^atenay Malabry, France)